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SSAT Middle Level Math : How to find a ratio

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Question #121 : How To Find A Ratio

What is the simplest form of the following ratio: 325:50?

Possible Answers:

26:1

1:26

1:13

13:2

Correct answer:

13:2

Explanation:

In order to determine the simplest form of a ratio, divide both sides of the ratio by a common factor. If we divide each side of this ratio by 5, we get 65:10.

This can still be simplified by dividing by 5 again.

Therefore, the simplest form of the ratio is 13:2.

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Example Question #1 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown molding to use as accent pieces. He needs $18\textup{ inches}$ of the molding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$3 \tfrac{1}{2} \textup{ feet}$

$2 \tfrac{3}{4} \textup{ feet}$

$1 \tfrac{2}{3} \textup{ feet}$

$1 \tfrac{1}{2} \textup{ feet}$

$2 \tfrac{1}{2} \textup{ feet}$

Correct answer:

$1 \tfrac{1}{2} \textup{ feet}$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $18\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$18\ inches:x\ feet\rightarrow \frac{18\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{18\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=18\ inches \times (1\ foot)$

Simplify.

12x=18

Divide both sides by .

$\frac{12x}{12}=\frac{18}{12}$

Solve.

$x=1 \tfrac{1}{2} \ feet$

The carpenter needs $1 \tfrac{1}{2} \ feet$ of material.

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Example Question #481 : New Sat

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $144\ inches$ of the moulding for the house. How many additional feet of the material will he need to purchase to finish the model?

Possible Answers:

Correct answer:

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $144\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$144\ inches:x\ feet\rightarrow \frac{144\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{144\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=144\ inches \times (1\ foot)$

Simplify.

12x=144

Divide both sides by .

$\frac{12x}{12}=\frac{144}{12}$

Solve.

$x=12 \ feet$

The carpenter needs $12 \ feet$ of material. Since he already has 8 feet he will need to purchase more to finish the project.

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SSAT Middle Level Math : How to find a ratio

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #121 : How To Find A Ratio

Example Question #1 : Solving Word Problems With One Unit Conversion

Example Question #481 : New Sat

All SSAT Middle Level Math Resources

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